WALLACE, WILLIAM (1768-1843), mathematician, was born on September 23, 1768, at Dysart, in Fife-shire, where Ile received his school education. In 1784 his family removed to Edinburgh, where he himself was set to learn the trade of a bookbinder ; but his taste for mathematics had already developed itself, and he made such use of his leisure hours that before the completion of his apprenticeship he had made considerable acquirements in geometry, algebra, and astronomy. He was further assisted in his studies by Professors Robison and Playfair, to whom his abilities had become known. After various changes of situation, dictated mainly by a desire to gain time for study, he became assistant teacher of mathematics in the academy of Perth in 1794, and this post he exchanged in 1803 for a mathematical mastership in the Royal Military College at Great Marlow (afterwards at Sandhurst). In 1819 he was chosen to succeed Playfair in the chair of mathematics at Edinburgh, and in 1838, when compelled by ill-health to retire, lie received a Government pension for life. He died in Edinburgh, after a lingering illness, on April 28,1843.

In his earlier years Wallace was an occasional contributor to Leybo tune's Muthematic«I Ileposilory and to the Gentleman's _Mathematical Companion. Between 1801 and 1810 he contributed the articles "Algebra," "Conic Sections," "Trigonometry," and several others in mathematical and physical science to the fourth edition of the Encycloyetlia Britannica, and some of these were retained in subsequent editions from the fifth to the eighth inclusive. Ho was also the author of the principal mathematical articles in the Edinburgh Eneyeloinnlia, edited by Brewster (1808-30). Subjoined is a list of his more important papers contributed to the Transactions of the Royal Society of Edinburgh : - " Geometrical Porisms, with Examples of their Applications to the Solution of Problems" (1796); "A new Method of expressing the Coefficients in the Development of the Formula which represents the Mutual Perturbation of two Planets" (1802); " New Serie.s for the Quadrature of the Conic Sections, and the Computation of Logarithms" (1808); "Investigation of Formuhe for finding the Logarithms of Trigonometrical Quantities from one another" (1823); "Account of the Invention of the Pantograph, and a Description of the Eidograph," the latter being an instrument of his own invention (1831); "Analogous Properties of Elliptic and Hyperbolic Sectors" (1839); and "Solution of a Functional Equation, with its Application to the Parallelogram of Forces and the Curve of Equilibration." In 1836 lie contributed "Two Elementary Solutions of Kepler's Problem by the Angular Calculus" to the Royal Astronomical Society; and for the Cambridge Philosophical Society he wrote a Paper on "Geometrical Theorems and Formul, particularly applicable to some Geodetical Problems."